In a propagating sinusoidal linearly polarized electromagnetic plane wave of a fixed frequency, the Poynting vector always points in the direction of propagation while oscillating in magnitude. The time-averaged magnitude of the Poynting vector is

In the last step, we used the equality \varepsilon_0\,\mu_0 = {c}^{-2} . Since the time- or space-average of \cos^2\left(\omega\,t-{\mathbf k} \cdot {\mathbf r}\right) is \textstyle\frac{1}{2}, it follows that

\left\langle S \right\rangle = \frac{\varepsilon_0 c}{2} E_0^2.

E= speedlight*B

The time averaged Poynting vector is equal to epsilonfreespace*speedlight*E^2/2

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